Steady-State Mixed Flow Reactors

The performance equation for the mixed flow reactor is obtained from Eq. 4.1, which makes an accounting of a given component within an element of volume of the system. But since the composition is uniform throughout, the accounting may be made about the reactor as a whole. By selecting reactant A for consideration, Eq. 4.1 becomes 

As shown in Fig. 5.3, if AO UqCao is the molar feed rate of component A to the reactor, then considering the reactor as a whole we have 

Introducing these three terms into Eq. 10, we obtain 

More generally, if the feed on which conversion is based, subscript 0, enters the reactor partially converted, subscript /, and leaves at conditions given by subscript /, we have 

For the special case of constant-density systems = 1 - in which 

---

For the simple steady-state, mixed-flow reactor (CSTR), da Jdt = 0, F = I, Q — and Equation 4.71 (Chapter 4) is recovered. Written in terms of conversion, this equation becomes... 

Nassar et al. [10] employed a stochastic approach, namely a Markov process with transient and absorbing states, to model in a unified fashion both complex linear first-order chemical reactions, involving molecules of multiple types, and mixing, accompanied by flow in an nonsteady- or steady-state continuous-flow reactor. Chou et al. [11] extended this system with nonlinear chemical reactions by means of Markov chains. An assumption is made that transitiions occur instantaneously at each instant of the discretized time. 

The main conclusions to be drawn from this study are that the reactor design works well, and that steady state continuous flow operation requires excellent mixing of the gases and two liquid phases and high conversions. Improvements in the catalyst (ligand) are required to reduce leaching still further, but commercialisation will also require a different reactor design or more than one CSTR in series. 

The other ideal steady-state flow reactor is called the mixed reactor, the backmix reactor, the ideal stirred tank reactor, the C " (meaning C-star), CSTR, or the CFSTR (constant flow stirred tank reactor), and, as its names suggest, it is a reactor in which the contents are well stirred and uniform throughout. Thus, the exit stream from this reactor has the same composition as the fluid within the reactor. We refer to this type of flow as mixed flow, and the corresponding reactor the mixed flow reactor, or MFR. 

The aqueous decomposition of A is studied in an experimental mixed flow reactor. The results in Table P5.25 are obtained in steady-state runs. To obtain 75% conversion of reactant in a feed, C o = 0.8 mol/liter, what holding time is needed in a plug flow reactor ... 

Reactant A (A R, C o = 26 mol/m ) passes in steady flow through four equal-size mixed flow reactors in series (r otai = 2 min). When steady state is achieved the concentration of A is found to be 11, 5, 2, 1 mol/m in the four units. For this reaction, what must be so as to reduce from... 

From steady-state kinetics runs in a mixed flow reactor, we obtain the following data on the reaction A R. 

The kinetics of the aqueous-phase decomposition of A is investigated in two mixed flow reactors in series, the second having twice the volume of the first reactor. At steady state with a feed concentration of 1 mol A/liter and mean residence time of 96 sec in the first reactor, the concentration in the first reactor is 0.5 mol A/liter and in the second is 0.25 mol A/liter. Find the kinetic equation for the decomposition. 

Using a color indicator which shows when the concentration of A falls below 0.1 mol/liter, the following scheme is devised to explore the kinetics of the decomposition of A. A feed of 0.6 mol A/liter is introduced into the first of the two mixed flow reactors in series, each having a volume of 400 cm. The color change occurs in the first reactor for a steady-state feed rate of 10 cmVmin, and in the second reactor for a steady-state feed rate of 50 cm /min. Find the rate equation for the decomposition of A from this information. 

In a series of steady-state flow experiments (Cao = 100, Crq = C o 0) in a laboratory mixed flow reactor the following results are obtained ... 

Plug-flow tubular reactor (PFTR) This reactor is operated under steady-state condition. The reactor is of tubular shape, the reactants enter at the inlet and the composition is a function of the distance from the inlet. However, the composition is not a function of time. The ideal plug-flow reactor is characterized by the absence of mixing in the direction of flow and complete mixing in the transverse direction. 

For a steady-state perfectly mixed flow reactor the energy balance can be made over the complete reactor ... 

The stirred-iank reactor may be operated as a steady-state flow type (Fig. 3-lu), a batch type (Fig. 3- b), or as a non-steady-state, or semibatch, reactor (Fig. 3-lc). The key feature of this reactor is that the mixing is complete, so that the properties of the reaction mixture are uniform in all parts of the vessel and are the same as those in the exit (or. product) stream. This means that the volume element chosen for the balances can be taken as the volume V of the entire reactor. Also, the composition and temperature at which reaction takes place are the same as the composition and temperature of any exit stream. 

This qualitative explanation for the oscillatory behavior of the particle number density is supported by theory. Assume the system can be modeled as a continuous steady state stirred tank reactor (CSTR) that is, reactants enter and products leave from a perfectly mixed tank with composition equal to that of the products. The set of equations derived in the previous section applies, but a new term must be subtracted from the right-hand side in each case to account for the loss of particles from the CSTR by the flow process. Equation (10.49) for the change in aerosol surface area with time becomes... 

For prediction of subassembly coolant flow rate and temperature distributions a wide range of coolant flow and thermal convection regimes must be considered including laminar and turbulent flow natural, forced and mixed (forced + natural) convection and steady state and transient reactor conditions. 

Mixed flow reactor experiments are relatively difficult to design and execute but they produce data that are easy to analyze. When the experiment reaches steady state, the concentration of all species in the reactor is constant. This means that the rate of species accumulation is zero, so the rate of generation is the difference between the input rate, which is the flow rate (g, kg/sec) multiplied by the feed concentration (m, , mol/kg), and the output rate, which is the flow rate multiplied by the effluent concentration (m mol/kg). 

Rimstidt and Newcomb (1993) performed an experiment to measure the rate of pyrite reaction with ferric iron in a mixed flow reactor. The reactor, containing 2 g of pyrite with a speciflc area of 0.047 mVg, was fed by a 1.0 x 10 m solution at a flow rate of 2.70 x 10 kg/sec. After a time, the experiment reached steady state where the concentration of Fe in the effluent solution maintained a constant value of 1.86 x 10 molal. 

Reaction rates can be determined from mixed flow reactors operating under non-steady state conditions using the following procedure. Material balance as defined by Eq. (4.1) requires that the rate of generation of a species by a reaction mol/sec) equals the rate of output mol/sec) minus the rate of input (j, mol/sec) plus the rate of accumulation mol/sec) in the reactor. 

The simplest box model consists of one reservoir that is fed by a constant flux (Fg) (Figure 8.2). The flux out of a reservoir is the product of the mass of the substance (A/) in the reservoir and a mass transfer constant (k). Box model reservoirs are simply gigantic ideal mixed flow reactors (see Chapter 4) where there is no net generation or consumption of the substance. Over geologic time spans these reactors tend to attain a steady state so that the flux into a reservoir is matched by the flux out, which means that the rate of accumulation in the reservoir is zero and M is constant (M j). The flux out of the reservoir equals a mass transfer constant (k, yr ) times the mass of the substance in the reservoir. 

If A > 1, the trace element is enriched in the solid relative to the solution during precipitation, so ntxJmM is reduced as precipitation proceeds. If A < 1, the trace element is enriched in the solution relative to the solid during precipitation, so mjjm increases as precipitation progresses. In a mixed flow reactor operating at a steady state, remains constant and the... 

In a mixed flow reactor operating at steady state, the concentrations of Tr and Min the solution are constant. This means that the composition of the solid is also constant. XJX reflects the relative rates of removal of the trace and major elements from the solution. These rates are the difference between the concentration of the element in the feed and effluent solutions multiplied by the flow rate (Q, kg/sec) through the reactor. 

SSITKA experiments can be performed in plug flow or mixed flow reactors. This approach was proposed by Happel et al. [18] and further developed by Beimett [19], Biloen [20], and Shaimon and Goodwin [21]. In these experiments a step change or pulsed input is induced in the isotopic label of one reactant in the reactant flow. The total concentration of labeled plus non-labeled reactants, adsorbates, and products is maintained at steady state under isothermal and isobaric conditions. The reactor effluent species are then monitored versus time. The mean surface residence time and abundance of adsorbed surfece... 

Basic PFR equation Design equations Nonisothermal operation Perfectly mixed flow reactor (MFR) Basic CSTR equation Nonisothermal operation Multiple steady states MSS In a CSTR Adiabatic CSTR... 

Methods accounting for mixing are most easily illustrated for steady state or stationary reactor operation, as in Fig. 12.3-1. Because of its stochastic nature, turbulent flow is in fact only statistically iiormy. The random behavior of the variables results in rapid fluctuations of their values around mean or so-called Reynolds-averaged, "steady state" values. Nevertheless, turbulent flow is governed by deterministic equations, the Navier-Stokes equations, whose terms have been explained in Chapter 7 and in which a transient term is included to account for the fluctuations around the statistically steady state values. 

---